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Alain Connes criticism of the mathematics system in America

  1. Aug 27, 2008 #1
    From this article: http://www.ipm.ac.ir/IPM/news/connes-interview.pdf
    Around pages #32-33 he makes the following comments:

    You were criticizing the US way of doing research and approach to science
    but they have been very successful too, right? You have to work hard to get
    tenure, and research grants. Their system is very unified in the sense they
    have very few institutes like Institute for Advanced Studies but otherwise
    the system is modeled after universities. So you become first an assistant
    professor and so on. You are always worried about your raise but in spite of
    all these hazards the system is working.
    I don’t really agree. The system does not function as a closed system. The
    US are successful mostly because they import very bright scientists from
    abroad. For instance they have imported all of the Russian mathematicians
    at some point.
    But the system is big enough to accommodate all these people this is also a
    good point.
    If the Soviet Union had not collapsed there would still be a great school of
    mathematics there with no pressure for money, no grants and they would
    be more successful than the US. In some sense once they migrated in the
    US they survived and did very well but I believed they would have bloomed
    better if not transplanted. By doing well they give the appearance that the
    US system is very successful but it is not on it’s own by any means. The
    constant pressure for producing reduces the “time unit” of most young people
    there. Beginners have little choice but to find an adviser that is sociologically
    well implanted (so that at a later stage he or she will be able to write the
    relevant recommendation letters and get a position for the student) and then
    write a technical thesis showing that they have good muscles, and all this in a
    limited amount of time which prevents them from learning stuff that requires
    several years of hard work. We badly need good technicians, of course, but
    it is only a fraction of what generates progress in research. It reminds me of
    an anecdote about Andre Weil who at some point had some problems with
    elliptic operators so he invited a great expert in the field and he gave him the
    problem. The expert sat at the kitchen table and solved the problem after
    several hours. To thank him, Andre Weil said “when I have a problem with
    electricity I call an electrician, when I have a problem with ellipticity I use
    an elliptician”.
    From my point of view the actual system in the US really discourages
    people who are truly original thinkers, which often goes with a slow maturation
    at the technical level. Also the way the young people get their position
    on the market creates “feudalities” namely a few fields well implanted in key
    universities which reproduce themselves leaving no room for new fields.
    In the US there are so many mathematicians. Their system produces about
    1200 new PhD’s a year.
    And they can’t find a position unless they belong to a field with the stamp
    of approval.
    This is massive! astronomical!
    But the problem is that whether or not they will find a position depends on
    whom will write their recommendation letters. I am not saying what kind of
    letter they will get since all these letters look alike in their emphatic style.
    The result is that there are very few subjects which are emphasized and keep
    producing students and of course this does not create the right conditions
    for new fields to emerge. At least in France, if you have a position in CNRS
    you are allowed to do whatever you want and people are given the maximum
    freedom of thinking without any unhealthy social pressure to work in this or
    that field if one wants to secure one’s future!

    What do you guys think about this?

    I personally think Alain Connes brings up some good points.

    But what other system is there? Alain Connes is fortunate to have a job where he only teaches 18 hours a year. Him and only 3 other mathematicians have this kind of position at College de Frances (I believe Serre, Yoccoz, and another famous mathematician). I guess the analogous institution in America would be the IAS near Princeton. Alain Connes is also a Fields Medalist and can pretty much get what he wants in terms of a job and or teaching hours.
    Last edited by a moderator: Apr 23, 2017
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  3. Aug 27, 2008 #2
    I believe he is right. (he is french, so you know I will side with him ;) ).

    But towards the topic; He takes up the very thing that is one of the greatest things with america, their braindrain of the entire world for the best minds that the world can offer. In the meantime, this takes the pressure of their indigenous people (the americans) which mean they get a carte blanche to be the worlds douchebags and idiots. Of course this is very generalising and there are americans that stand out of the crowd, but a country with less than 100 in median IQ doesn't impress.
  4. Aug 27, 2008 #3

    Andy Resnick

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    Connes raises issues that are true in fields besides Mathematics. Pretty much the entire University system is open to the same criticisms (pressure for money, sociologically well-implanted advisors, etc).

    There are a lot of good things about the US system- the competition for grant dollars and permanent positions results in generally high levels of scientific quality. To be sure, there are side effects-feudalism, for example- but on balance the system works well enough.

    I note that Connes does not offer any alternatives (unless it's in part of the article not quoted). Simply increasing the amount of available dollars is not the answer, either, IMO- that's simply welfare by another name.
  5. Aug 29, 2008 #4
    I admit to being VERY euro-centric. But on this one my euros is on monsieur Connes.

    Andy_Resnick: You are correct in that he doesn't bring up an alternative. But I think the alternative actually lies in the private industry. Many europeans believe the state should take care of everything, something I am very opposed to. But I also think that the american system has great flaws as well, although you get more bang for the buck (or at least that is my personal views on your system of scientific funding).

    But let's take a look at the google corporation. It's a very big corporation, a large behemoth in it's field, and has risen to that in only a couple of years. They don't have especially impressive products atm, but they one thing that is so mind-awing and inspiring to everyone with a little sense of entrepreneuring. They as a private enterprise actually takes fifteen percent of paid employee-time and let them do what they wish with the time. This often is counterproductive in the short run of the company, they lose money by the hour, but they gain in a more creative work enviroment, where ideas is exchanged freely and true genious can grow and cross-pollinate across the entire global company.

    Sure, you may think this is a new thing and will be doomed like a dragonfly. But look at bell labs, a bit different but all the same, 6 (!) nobelprices from a private research institute. Or look at the skunkworks at boeing, they helped the western alliance win the cold war.

    to summarize; the funding situation is critically bad, it invests in the same regurgitation all over again, sure people learn the skills and methods of being a phd/associate professor, even professor and leader in the chosen field. But to actually bring something historically worthwhile from these european and american systems, give me a break, they are flawed dinosaurs that needs to be broken down and replaced by new, better and more efficient systems.

    In writing this, I know it maybe will upset people. But I mean no harm or to upset, just to bring a little point of view into it that is often forgotten.
  6. Aug 29, 2008 #5


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    i agree with much of connes criticism, but on second thought it is also nonsense to compare the freedom of a very few top people in france against the pressure placed on low level people in the US like me for example. i think we also have cushy jobs for the scientific elite. at least i think our fields medalists are well treated.

    but i have heard for years from french people that the US system does not respect the scientific mind, but overworks us in teaching elementary courses. I have indeed often felt this was true. it would help to have more specific comparisons.

    perhaps this is just another aspect of the class system of europe against the egalitarian system in the US. i.e. we send everyone to college and expect highly trained scientists to teach the most ill prepared freshmen. i speak from experience here as i am currently teaching a calculus class to many very ill prepared but bright young people.

    my impression is that in europe students who do not like academics go instead to trade school.
    Last edited: Aug 29, 2008
  7. Aug 29, 2008 #6
    The problem with private industry is that Google's engineers don't use their 15% to work on topological quantum field theory; the guys at Skunkworks aren't into n-categories; Bell Labs isn't even comparable to the place it was 40 years ago. Industry isn't going to be cutting throats to build the next big particle accelerator... It's just not good for the bottom line. This is exactly the problem that Connes has with the American university system - that even the blue sky research you do is doomed unless it's mainstream.

    What I disagree with Connes about, and maybe I'm missing the point, is his complaint that America is only successful because we import the best and brightest minds. I don't see why this is a problem though. I've not met any American scientists who are unqualified, and certainly none who've lost jobs to less qualified "imports," so if we have the space and money for them, what's wrong with bringing them in? Should we not? Are we supposed to cripple ourselves just to prove Alain Connes is right?
  8. Aug 29, 2008 #7
    I've heard some people argue for a similar argument to Connes's by pointing out that most of the Fields Medalist were not Americans.

    BUT, a few of them, off the top of my head were American educated, at least PhD wise. Terrence Tao certainly was, S.T. Yau is another example.

    What exactly is the difference between the US system and the European system? The Russian system or the old USSR system? Specifically, what do they do differently for undergrad math and what do they do differently for grad students? Can anyone clarify that? I have no idea how the education system is or was in western Europe and the USSR.
    *I understand it's tough to give such sweeping general statement about a whole continents educational system, but what is the perspective of a European critiquing the American system and vice versa?

    I do remember looking over the Math in Moscow UG program and I was really surprised by the level of the coursework that was being taught. But perhaps in Russia they also teach calculus and physics to high school students earlier.
  9. Aug 29, 2008 #8


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    in a sense it is supply and demand. if lots of brilliant scientists want to live here, and they pour in from abroad clamoring for our professorial positions, then our profit oriented system is not going to make the life of a scientist cushy, just the opposite.
  10. Aug 29, 2008 #9


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    off the top of my head, american fields medalists: david mumford, curt mcmullen, stephen smale, jesse douglas, ed wittten, ...(there are 11 in all),

    i guess some others that come to mind are not born here but did choose to live and work here at least some of the time, like lars ahlfors, heisuke hironaka, vaughn jones, shigefumi mori,..... even serre has visited here often.

    actually the US apparently has more fields medalists than any other country, even though it is true that american fields medalists are not a majority of all of them, they are nonetheless a plurality.
    Last edited: Aug 29, 2008
  11. Aug 29, 2008 #10
    If lots of brilliant scientists from abroad want to live here, doesn't that reflect more poorly on the Russian/French/Whatever system than on the U.S. one? I mean, I understand that it makes science a quickly saturating profession, and much harder on scientists than it should be - I just don't see why it's an indictment of the way the system is. Isn't it that way everywhere?
  12. Aug 29, 2008 #11
    My general perception is that a recent math phd will have an extremely difficult time obtaining a tenure track position at a PhD granting math program. I would expect it to be easier as the supposed reputation of the program decreases, but it still seems incredibly difficult.

    However, why is this a bad thing? Why is it a bad thing to have so many qualified applicants for these tenure track jobs?

    I think the bad thing is the publish or perish mentality, I'm not sure if this is only restricted to the US or if this is also prevalent in Europe. But I think the publish or perish issue is a big one. For example, Andrew Wiles had to consistently publish little papers as he was working on the proof of Fermat's Last Theorem. Perelman worked for almost a decade to give a proof of the Thurston Geometrization Conjecture.

    I have been actively looking at various math faculties, their research, their publications (both recent and from the past) and I am shocked to see such a dearth of activity in a lot of fields of mathematical physics. I saw very few if any (although in my admittedly not thorough or rigorous study) mathematicians working on putting quantum field theory on a rigorous foundation or making any headway on the Yang Mills Mass Gap Hypothesis.

    There are a few possiblities:
    1) Mathematicians do not care about those problems. OK, totally acceptable, nobody should be forced to work on these problems. However, I don't know if this is the case.
    2) The aforementioned problems might take years, even decades with the possibility of the end result being complete failure and nonsense. So again, maybe mathematicians do not want to invest the time for what might be an enormous effort and what time turn out to be an enormous time commitment.
    3) Mathematician's do not want to risk their career working in the "Wild West" - i.e. problems that are very difficult, do not have strong foundational roots in well established fields of mathematics and or do not have an active research community, this mostly applies to PhD students, recent PhD's and PhD's looking for tenure.

    However I remember what Michael Atiyah said in a paper that was a response to one of Jaffe's papers on constructive quantum field theory. Atiyah admits that it is a huge risk to one's career, but you get to work on a fundamentally important subject. A quote from Atiyah's paper entitled: "RESPONSES TO “THEORETICAL MATHEMATICS: TOWARD

    "What we are now witnessing on the geometry/physics frontier is, in my opinion,
    one of the most refreshing events in the mathematics of the 20th century. The
    ramifications are vast and the ultimate nature and scope of what is being developed
    can barely be glimpsed. It might well come to dominate the mathematics of the
    2lst century. No wonder the younger generation is being attracted, but Jaffe and
    Quinn are right to issue warning signs to potential students. For those who are
    looking for a solid, safe PhD thesis, this field is hazardous, but for those who want
    excitement and action it must be irresistible."
  13. Aug 29, 2008 #12


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    I heard recently, and posted somewhere, than more than half of MS degrees in science and engineering at US universities go to foreign students, and a substantially larger fraction of PhD's (S & E) from US universities go the foreign grad students.

    What that tells me is that foreign universities seem to do a better job of preparing students for advanced degrees, or a large portion of US students are less inclined to get advanced degrees, or are more concerned about a job.

    If US students are less inclined, is that because they cannot handle the rigors of advanced degrees, and is that because the US high schools and university undergrad programs simply don't prepare students for advanced degrees?
  14. Aug 29, 2008 #13
    Fields Medalist

    When a mathematician is put under the heading of Europe or America, that means mainly educated in that region (i.e. did undergrad and grad in Europe or America)

    Europe (Germany, France, UK, Netherlands, etc): Werner, Lafforgue, Wiles, Gowers, Borcherds, Yoccoz, Lions, Bourgain, Jones (NZ), Faltings, Donaldson, Connes, Deligne, Mumford, Bombieri, Baker, Atiyah, Grothendieck, Hörmander, Thom, Roth, Serre, Selberg, Schwartz, Ahlfors
    America: McMullen, Witten, Freedman, Thurston, Quinlann, Fefferman, Thompson, Milnor, Smale, Cohen, Douglas
    Asia (Japan, China, Korea, India, etc.): Mori, Hironaka, Kodaira,
    Russian/Soviet: Perelman, Okounkov, Voevodsky, Kontsevich, Zelmanov, Drinfield, Novikov, Margulis,
    Mix of non USA undergrad/USA grad: Tao, S.T. Yau

    My reference: http://en.wikipedia.org/wiki/Fields_Medal

    So that is 25 Euro, 11 American, 3 Asian (all from Japan), 8 Russian/Soviets, 2 with non-USA undergrad but got their PhD in America.

    (Not that this is proof the American mathematics system is flawed, but it is an interesting thing to note nonetheless IMO).

    Note: I only lumped in all the European countries to keep on topic, I by no means am implying that the education system in France is the same as in the UK or Germany.
    Last edited: Aug 29, 2008
  15. Aug 29, 2008 #14


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    I SUPPOSE you know wiles has been at princeton much of his career, including the time he spent solving the fermat conjecture. so he was presumably enjoying the benefits of the american system then.
  16. Aug 29, 2008 #15
    Yes but I said I classified him as European because that's where he was educated up to looking for a teaching/research position. So I don't quite see the point, if there is one? I said that I classified fields medalists in terms of where they were educated, which is one of the main points of Connes critique.
  17. Aug 29, 2008 #16
    If I may interject my own opinion on this matter... first, there are over 2 billion Indian/chinese people, so is it really a surprise that there are a heck of a lot of them over here in the U.S. which holds probably 80% of the top 10 universities in math/science/technology? Gosh... in some of my grad classes at my uni (Georgia Tech) I am one of maybe 5 Caucasians out of a class of 50 if it's a class related to computers or semiconductor devices. Interestingly enough, there are only a few asians in my electromagnetics class.

    It goes deeper than that though. Consider this research done by ETS regarding select survey questions that ask why caucasians/asians want to pursue graduate work ( http://www.ets.org/Media/Research/pdf/RR-96-25-Grandy.pdf ). Asian students clearly feel compelled by societal factors to pursue graduate work while Caucasians seem to do it more for reasons of personal interest. To Asians, getting a PhD is something you "have" to do, so they get it and are miserable while doing so, but the consequences of not getting one are perceived as hefty. This is the core reason I think for why so many Chinese/Indians are here.
  18. Aug 30, 2008 #17
    I could use the argument that we don't know what they do with the time. But, look at the opportunities instead. Maybe not all of the scientists would like to work into fundamental work, but at a corporation with maybe 20k employees, but if only 1% did it (I actually believe this figure to be higher because of the many mathematicians that work at google) it would mean 200 fundamental researchers. Which is a lot.

    Yes industry is never going to pursue big science. That is LHC and other such stuff. That is sorry to say something that has to be publicly state-funded in this economic situation we are in. But industry can do a lot of things that doesn't require a commitment of that magnitude, bell labs has shown that. Even If I admit to it that they maybe are a bit old now and it was probably right to close down the institute, even if I got a bit agitated about that.

    Besides my point was that being a big importer of scientists, does only mean that americans can slack of more. They don't need to apply themselves to hard subjects or do things that are particularly difficult. Because they buy that instead of developing the resource at home. A free jobmarket with a high mobility is very benificial towards scientists because they apply themselves all the time, it's their job. :) (I am pro importing and exporting science all over the world, because science is the light with we can extinguish prejudice, religion and other superstitions). And besides, most european scientists stay in europe or go to asia.

    Let's look at the facts. at OECD [1] you can see what the differences really are between europe, japan and the US. In Europe the funding comes from the state (although private enterprise-R&D comprise along the lines of 60%) which comes with inefficiency and other jummy state-detractors. In the US, most research is privately funded, or along the lines of 75%. Which means it's more efficient and application-oriented.

    But there is a very large difference between europe and the États-Unis. In the US, Almost more than 20% of ALL research go into the arms industry. I am by no means a pacifist, believe that people have a right to defend themselves, but come on, 20% of all research budgets go into armaments, defence and stuff like that. I do not believe that arms industry research is more efficient than the staterun research. in terms of efficiency, private > State > Armed forces. It applies to almost every country. Besides, we cannot eat munitions, we cannot produce more luxury with military grade planes and can certainly not drive around in a city or transport goods with an aircraft carrier.

    Another point in the matter is, I don't care where the research takes place. If India produces a nobelprice per year, or china takes the next twenty fields medals, or Europe becomes the industrial high tech motor of the world. Whatever, really! That which matter is that somewhere we must try to get more funding and room for fundamental research at the highest level. Getting more dough for applied research as well which is not arms-related (in my opinion it's just a waste of money and effort). Efficient undergrad-teaching and research is a must for the human civilization to not stagnate and go backwards.

    [1] Main science and technology indicators 2008-1 http://www.oecd.org/dataoecd/49/45/24236156.pdf [Broken] (downloaded on 2008-08-30)
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  19. Aug 30, 2008 #18


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    well I read connes remarks differently. it seemed to me he was primarily criticizing the climate in the US for doing research, saying that the pressure reduces the chance for innovation, which makes it odd that so many researchers choose to work here. so to me the case of wiles is a direct contradiction to the claim. or maybe connes thinks the conditions under which wiles worked should have been even much better.
    Last edited: Aug 30, 2008
  20. Aug 30, 2008 #19
    Organizations such as DARPA are considered defense but consider that they originally funded ARPANET and GPS among other things. Fundamental research? No, but it's fairly easy to add spin to a new project idea to aim it at defense crowds to get funding.
  21. Aug 30, 2008 #20
    jhicks: So you can trick the Defense community into funding other stuff that will benefit humanity a lot more than the defense community? intriguing if I got you right.
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